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Title: Singular conditional autoregressive Wishart model for realized covariance matrices Authors:  Taras Bodnar - Stockholm University (Sweden)
Gustav Alfelt - Stockholm University (Sweden)
Joanna Tyrcha - Stockholm University (Sweden)
Farrukh Javed - Lund University (Sweden) [presenting]
Abstract: Realized covariance matrices are often constructed under the assumption that the richness of intra-day return data is greater than the portfolio size, resulting in nonsingular matrix measures. However, when for example, the portfolio size is large, assets suffer from illiquidity issues, or market microstructure noise deters sampling on very high frequencies, this relation is not guaranteed. Under these common conditions, realized covariance matrices may obtain as singular by construction. Motivated by this situation, we introduce the Singular Conditional Autoregressive Wishart (SCAW) model to capture the temporal dynamics of time series of singular realized covariance matrices, extending the literature on econometric Wishart time series models to the singular case. This model is furthermore developed by covariance targeting adapted to matrices and a sector-wise BEKK-specification, allowing excellent scalability to large and extremely large portfolio sizes. Finally, the model is estimated to a 20-year long time series containing 50 stocks and to a 10-year long time series containing 300 stocks, and evaluated using out-of-sample forecast accuracy. It outperforms the benchmark models with high statistical significance and the parsimonious specifications perform better than the baseline SCAW model, while using considerably fewer parameters.